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** **__DC CIRCUITS class 11 Notes__

__DC CIRCUITS class 11 Notes__

·
**Electric circuits**

The rate of flow of charge is known as electric circuits. If Q be the
charge that flows through any cross-section area in time ‘t’. Then,

electric current (I)=Q/t

· **Charge carrier**Solid-free electron

liquid- ions

gas – ions and free electrons

semiconductor – holes and free electrons

·
**Types of current **

**1) Direct current**

The type of current whose magnitude and direction remain constants at all time is called direct current.

2) Alternating current

Types of current whose magnitude and direction changes with respect to
time is called alternating current.

·

**Ohm’s law**

Its states that ‘the current flowing through conductors is directory
proportional to the potential difference across its end, the external
conditions remain constant.’

I.e.

V𝞪I

V= RI

Where R is the proportionality constant and is called electric
resistance.

· **Drift velocity**

Drift velocity is the average velocity acquired by the free electrons in
a conductor subjected to an electric field.

I=V_{d}enA

is the relation between drift velocity and electric current

where, V_{d} - drift velocity

e - charge of an electron

n - no of electron
per unit volume

A - cross-section
area

· **Current density
**

The current density of a conductor is defined as the amount of current that
flows per unit area of the conductor. Its units is ampere per square
meter.

**Electrical Resistance**The property of a conductor by virtue of which it opposes the flow
of current through it is known as resistance. And the device is called
a resistor. It is denoted by R and the unit is Ohm (Ω). It is measured by the ratio of potential difference across its ends to
the current flowing through it.

R=V/I

**One Ohm:**The resistance of a conductor is said to be of one ohm if one ampere current flows through it under a potential difference of
one volt.

one ohm = 1 volt/1 Amphere

**Laws of resistance**Consider a conductor of length (l) and area of cross-section (A). Let R
be the resistance of the conductor. Experimentally it was found that
the resistance of the conductor is:

i. directly proportional to the length of the conductor.

i.e. R ∝ L……(1_)

ii. inversely proportional to the area of cross-section of the conductor.

i.e. ∝1/A……(_2_)

On combining (1) & (2), we get,

R ∝L/A

R =C *L/A

Where, р is the proportionality constant, called the resistivity or the specific resistance of the material of the conductor.

р
= RA/L

If L = 1m and A= 1m^{2}, then ,
р
=R

Thus, the resistivity of the material of a conductor is defined as the resistance of the conductor of unit cross-sectional area per unit length. Its unit is ohm meter (Ω m) in SI units.

__Ohmic and Non-Ohmic Conductors__

Ohmic ConductorsConductors which obey Ohm’s Law, have a constant resistance when
the voltage is varied across them or the current through them is
increased. These conductors are called ohmic conductors. A graph of the current vs the voltage across these conductors will be a
straight line. Some examples of ohmic conductors are tungsten resistors and nichrome wires.

**Non-Ohmic Conductors** Conductors who don't obey Ohm’s Law are called nonohmic
conductors. The current-voltage graph of a non-ohmic conductor is not a straight
line but is a curve. Electrolytes, vacuum tubes, junction diodes, transistors,
etc are some examples of non-ohmic conductors.

**Resistances in Series and Parallel**

1)
**Series combination of Resistances**

Resistances are said to be in series when they are joined end to end,
so that same current flows through each of them.

From Ohms law,

V_{1}
= IR_{1}V2= IR_{2}V_{3}
= IR_{3}

_{ }

If V be the potential difference across the whole combination, then,

V = V_{1}
+ V_{2}
+ V_{3}V = IR_{1}+ IR_{2}+ IR_{3}V= I(R
1+ R_{2}
+R_{3})

V/R= R_{1}
+ R_{2}
+ R_{3}
……(1_)

Let, R_{S}
be the effective resistance of the series combination, then,

V =IR_{s}……. .(_2_)

On comparing equations (1) and (2), we get,

R_{s}=R_{1}+R_{2}+R_{3}_{}

Thus, when the resistors are connected in series, the effective resistance of the combination is equal to the sum of resistances of individual resistors.

Properties of the series combination

• The same amount of current flows through all resistors

• The potential is divided and a potential difference is different
depending upon the resistance of the resistor

• The value of equivalent resistance is equal to the sum of
individual resistance.

• The value of equivalent resistance is greater than that of even
the greatest resistance.

**2) Parallel combination** The combination in which one
end of all resistors are connected with the positive terminal and another in of all resistors are connected
with the negative terminal of a battery so that voltage drop across each
resistance remains the same is known as a parallel combination of resistors.

Let us consider three resistors of resistance R1, R2 and R3 are connected in parallel combination with a battery of potential V. Since resistors are in parallel combination, so potential across each resistor is same (i.e. V).

Let I be the total current supplied by the battery. The current I is divided into I1, I2, and I3 and flows through R1, R2, and R3 respectively. Let Rp be the equivalent resistance of the circuit. Then,

I = I_{1}
+ I_{2}
+ I_{3}
……(_1)

From Ohm’s law, we have,

I_{1}
=V/R_{1}I_{2}
=V/R_{2}I_{3}= V/R_{3}

Substituting these in the above equation we get,

I =V/R_{1}+V/R_{2}+VR_{3}I/V=1/R_{1}+1/R_{2}+1/R_{3}
…….. (2)

Let R_{P}
be the equivalent resistance in this combination, then,

V=IR_{P}I/V= 1/R_{P}……..... (2)

From equations (1) and (2), we have,

1/R_{P}= 1/R_{1}+ 1/R_{2}+ 1/R_{3}

Thus, when resistors are connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of reciprocal of the resistance of individual resistors.

**Properties of parallel combination:**• The potential difference is the same across each resistor.

• The circuit is divided and the value of current is different depending upon the resistance of the resistor.

• The reciprocal of equivalent resistance is equal to the sum of the reciprocal of individual resistance.

• The value of equivalent resistance is less than that of even the smallest resistance.

**Voltage Divider Circuit** An electric circuit that contains a series combination of resistors is
known as a voltage divider circuit. Let R

_{1 }and R

_{2}resistors, connected in series. I remain constant in each resistor but the potential difference V provided by the cell is divided into each resistor. Let V

_{1}and V

_{2}be the potential difference across resistors with resistance R

_{1 }and R

_{2 }respectively.

Here the equivalent resistance is given by: R=R_{1}+R_{2}Total current = I

Thus, total voltage (V)=I(R_{1}+R_{2})

I=V/(R_{1}+R_{2})………(1)

Now, the Potential difference cross R_{1 }is given by :

V_{1}=IR_{1} …… (2)

Substituting (1) in equation (2), we get,

V_{1}={V/(R_{1}+R_{2})}*R_{1}

V_{1}={R_{1}/(R_{1}+R_{2})}*V

Similarly,

V_{2}={R_{2}/(R_{1}+R_{2})}*V

If the internal resistance is neglected, V is the sum of V_{1} and V_{2}.

**Current Divider Circuit**An electrical circuit that contains a parallel combination of resistors is
known as a current divider circuit. Let R1 and R2 be the resistances of two resistors connected in parallel. In the
circuit connection, the potential difference V in each resistor remains constant,
but the current I is divided into each part of a parallel circuit. Let
I1 and I2 be the current passing through resistors with resistances R1 and R2
respectively.

Here the equivalent resistance (R) is calculated as;

1/R = 1/R_{1 }+ 1/R_{2}

1/R
=(R_{1}+R_{2})/(R_{1}R_{2})

R=(R_{1}R_{2})/ (R_{1}+R_{2})

Now, the current passing through R_{1},

I_{1 }= V / R_{1}

I_{1} = IR / R_{1}_{}

I_{1}= (I/R_{1}) *
{(R_{1}R_{2})/ (R_{1}+R_{2})}

I_{1}= {R_{2}/ (R_{1}+R_{2})}*I

Similarly,

I_{2}= {R_{1}/ (R_{1}+R_{2})}*I

The total current (I) is the sum of I_{1 }and I_{2.}_{}

·
Potential difference and Energy

The potential difference between two points X and Y in an electric field. E
is given by the work done in moving a unit positive charge between these
points in an external circuit.

Potential difference = work done / charge carried

V = W / q_{0 }Dimensional formula for Volt (V)= [ML^{2} T^{-3}A^{-1 }]

·
Expression for heat developed in a resistor.

Let us consider an electric device, carrying a current I from end X to
Y

for time t. Let Q be the charge carried from end X to Y.

I = Q / t

Q = I *t

If W be the amount of energy liberated (heat, light, sound, mechanical

work etc) in time t, P.d (V) between the ends X and Y is given by,

V= W /
Q

W = Q*V

W = I*t*V

W = I^{2}Rt

Here, W may be the work done to transfer the charge from X to Y. In

passive resistor, all electrical energy is converted into heat energy
H.

H = I^{2}Rt =V^{2}t /
t

·
Electrical power

The electrical power of an electric device is defined as energy electrical liberated
for second in it.

Let, V be the potential difference across two ends A and B of a conductor and I be the current flowing through it for time t. Then electrical energy liberated is given by,

W = I^{2}Rt =IVt

Electrical power supplied is,

P = W / t = IVt / t = IV

In a passive resistor (that
converts all electrical energy into heat) of resistance R all the power
supplied appears as heat.

P = IV = I^{2}R =V^{2} / R

SI unit of power is watt (W). Kilowatt (KW) is larger unit of power.

One watt is power consumed in a device through which one ampere current flows through when a potential difference of one volt is maintained across it.

Electromotive force

To maintain continuous electric current in a closed circuit, it is
necessary to maintain a potential difference between any two points of the
conductor in the circuit. The devices, such as batteries for electric
generators are able to do so. The property of the devices which maintain
potential difference between two points of a conductor connected across it,
is called electromotive force (emf). The devices are called sources of emf
and are able to do work on the charge carriers, so a current flows through
the circuit.

The emf of a source is defined as the work done in moving a unit

positive charge from low potential to high potential end throughout the
circuit.

Let, W be the work done in moving a charge Q then, emf E of the

source is

E = W /
Q

SI unit of is volt (V). The potential difference between two poles of a
cell in an open circuit gives emf of a cell.

·
Internal resistance of a cell

The electrolyte between electrodes of the cell offers certain resistance.
when a current flows through it. This resistance is called the internal
resistance of the cell. It depends on the following factors.

i. It depends on the nature of the electrolyte

ii. It is directly proportional to the concentration of electrolytes

iii. It is directly proportional to the distance between electrodes

iv. It is inversely proportional to the area of electrodes inside
the electrolyte

v. It depends on the temperature of the electrolyte.

·
Terminal potential difference

The potential difference between two poles of a cell in a closed circuit is
called a terminal potential difference of the cell. It is equal to the total
potential difference across all the external resistance of the circuit. Relation between Internal resistance and Electromotive force of a
cell.
The internal resistance is connected in series with the resistance of the
external circuit.
In the above diagram, a cell of emf E and internal resistance (r) are
connected in
series with a key while a voltmeter is connected in parallel with the cell.
So, the
total resistance of the circuit is given by;

R_{TOTAL }= (R
+ r)

Normally, the value of internal resistance is very low. If the current in
the circuit

is I, then we get,

Total current = Total / Total resistance

I = E / ( R + r )

E = I ( R + r )

E = IR + Ir

E = V + Ir

E – V
= Ir………..(1)

Here, V and Ir are respectively the potential difference between the two
ends of the resistance of the external circuit and potential drop for r
inside the cell. V is called the terminal potential difference or
voltage.

That means V is the potential difference between the terminals of the cell
during the flow of current in the circuit.

From equation (1), it is clear that V < E.

The reason for the smaller value of terminal voltage than the electromotive
force is due to the fact that some energy is needed for the current to flow
through the internal resistance of the cell. As a result, a potential drop
takes place inside the cell. So it is seen that the potential difference
between the two terminals of a cell decreases by an amount of ‘Ir’, which
means ‘Ir’ amount of voltage does not contribute in the circuit, rather
becomes lost. For this reason, ‘Ir’ is called ‘lost volt’.

r= (E – V)
/ I =( E – V ) / (V/R)

r = {( E – V ) /
V } * R

This relation is known as circuit formula and gives the relation between
internal

resistance (r), emf (E), voltage (V) & Resistance (R)